Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Launch

10 minutes

Opener: As students enter the room, they will immediately pick up and begin working on the opener – Instructional Strategy - Process for openers. This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3.

Learning Target: After completion of the opener, I will address the day’s learning targets to the students. For today’s lesson, the intended target is “I can determine if a triangle can be created given angle and side measurements.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

While this lesson is an exploration of 7.G.2 - constructions, I have found that it really becomes an introduction to using a protractor. Though students should be proficient with the use of a protractor, I find that I have to walk around and help several students get it lined up correctly. Depending on the class, sometimes I am able to have student experts assist with using the tools, but not always. If the entire class lacks proficiency with the tools, this lesson may end up taking more than one day to complete. With the availability of so many computer programs that do the work for them, students do not have the proficiency with protractors that they should. Other than learning to use the tools appropriately (mathematical practice 5), the big take away from this lesson should be when given information about the sides or angles of a triangle, what combinations result in a unique triangle, no triangle, and what information forms more than one triangle.

Opener

Instructional Strategy - Process for Openers

Explore

Guided Notes: To activate prior knowledge and refresh students' memories on triangles, we are going to start with some basic notes about classifying triangles by their sides and angles. I am hoping to use mostly student input for this portion of the class - this information is certainly not new! After talking about classifying triangles, we will move into trying to construction triangles given certain information. I expect students to struggle with this, but I really want them working on learning about the available tools (MP 5) as well as perseverance (MP 1)! I will have them construct a triangle that has one side that is 4 cm and one 60 degree angle - and then they will compare with each other...is everyone's triangle exactly the same? NO! So there is more than one way to do this! Next they will move into a competition to see which table can make the next four constructions the fastest....only it is a trick! One of the triangles cannot be constructed! We will come back together as a class to go over the constructions and to complete a list of guidelines for when one, none, or many triangles can be formed.

Practice: With their table groups, students will work through problems, trying to construct triangles, or use their notes to determine if a unique triangle can be constructed or not. What is not finished in class will be homework.